What is it that Lagrangian density with only bilinear terms always corresponds to free field theory?

Question

Is there an intuitive proof of this fact? (Maybe connected in some way to Central Limit Theorem?).

score 7 · Accepted Answer · edited Feb 18 '15 at 20:59

7

Because that way the Euler-Lagrange equations turn out to be linear and thus the superposition principle holds. Superposition principle means "free theory".

edited Feb 18 '15 at 20:59

JamalS

19,254

answered Feb 18 '15 at 20:47

Valter Moretti

71,578

What is it that Lagrangian density with only bilinear terms always corresponds to free field theory?

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